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Perturbation to TBM mixing and its phenomenological implications

To accommodate the recently observed non-zero reactor mixing angle $θ_{13}$, we consider the lepton mixing matrix as Tri-bimaximal mixing (TBM) form in the leading order along with a perturbation in neutrino sector. The perturbation is taken to be a rotation in 23 plane followed by a rotation in 13 plane, i.e., $R_{23}(θ_{23}')R_{13}(θ_{13}',ϕ)$. We obtain the allowed values of the parameters $θ_{23}'$, $θ_{13}'$ and $ϕ$, which can accommodate all the observed mixing angles consistently and calculate the phenomenological observables such as the Dirac CP violating phase ($δ_{CP}$), Jarlskog invariant ($J_{CP}$), effective majorana mass $M_{ee}^ν$, and $m_{ν_e}$, the electron neutrino mass. We find that $δ_{CP}$ can take any values between $0$ and $-π/2$ and $M_{ee}^ν$ always comes below its experimental upper limit.